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Mathematics

A-Level Mathematics is the single unified qualification set against the Department for Education GCE AS and A level subject content and delivered through the AQA 7357 specification. It fuses a substantial core of pure mathematics with prescribed applied content in statistics and mechanics, and is threaded throughout by the three overarching themes of mathematical argument and proof, problem solving and mathematical modelling.

0/81 Texts·20 Chapters·~195 min total

Continue reading — Chapter ITable of contents
LPDfE GCE Mathematics OT1LPAQA 7357 OT1LPDfE GCE Mathematics OT2LPAQA 7357 OT2LPDfE GCE Mathematics OT3LPAQA 7357 OT3+60 more●●○Standard●○○Foundation●●●Advanced
Table of contents · 20 ChaptersT·20
Ch. IOverarching themes4 texts · 0 read
  • Mathematical argument, language and proof (OT1)Text L·01 · Recommended start3 min
  • Problem solving (OT2)Text L·023 min
  • Mathematical modelling (OT3)Text L·033 min
  • Notation, communication and the assessment objectivesText L·042 min
Ch. IIProof4 texts · 0 read
  • The language and structure of proofText L·053 min
  • Proof by deductionText L·063 min
  • Proof by exhaustion and disproof by counter-exampleText L·073 min
  • Proof by contradictionText L·083 min
Ch. IIIAlgebra and functions5 texts · 0 read
  • Indices and surdsText L·092 min
  • Quadratic functions and the discriminantText L·103 min
  • Equations, inequalities and polynomialsText L·113 min
  • Functions: composite, inverse and the modulusText L·123 min
  • Graphs, transformations and partial fractionsText L·132 min
Ch. IVCoordinate geometry in the (x, y) plane3 texts · 0 read
  • Straight lines and their equationsText L·142 min
  • The circle and its propertiesText L·153 min
  • Parametric equations of curvesText L·162 min
Ch. VSequences and series4 texts · 0 read
  • Sequences and recurrence relationsText L·172 min
  • Arithmetic sequences and seriesText L·182 min
  • Geometric sequences and seriesText L·192 min
  • The binomial expansionText L·202 min
Ch. VITrigonometry5 texts · 0 read
  • Radians, arcs and sectorsText L·212 min
  • Trigonometric graphs and exact valuesText L·222 min
  • Identities and reciprocal and inverse functionsText L·232 min
  • Compound- and double-angle formulaeText L·242 min
  • Solving trigonometric equationsText L·252 min
Ch. VIIExponentials and logarithms4 texts · 0 read
  • Exponential functions and the number eText L·262 min
  • Logarithms and the laws of logsText L·272 min
  • Solving exponential equationsText L·282 min
  • Modelling with exponentials and log-linear graphsText L·293 min
Ch. VIIIDifferentiation4 texts · 0 read
  • The derivative and first principlesText L·302 min
  • Rules of differentiationText L·312 min
  • Stationary points and curve analysisText L·323 min
  • Implicit, parametric and connected ratesText L·333 min
Ch. IXIntegration4 texts · 0 read
  • Indefinite integration and standard resultsText L·342 min
  • Definite integrals and areasText L·352 min
  • Techniques: substitution and by partsText L·362 min
  • Differential equationsText L·372 min
Ch. XNumerical methods4 texts · 0 read
  • Locating roots by change of signText L·382 min
  • Fixed-point iterationText L·392 min
  • The Newton-Raphson methodText L·402 min
  • The trapezium ruleText L·412 min
Ch. XIVectors4 texts · 0 read
  • Vectors, notation and magnitudeText L·422 min
  • Vector arithmetic and unit vectorsText L·432 min
  • Position vectors and geometryText L·442 min
  • Vectors in three dimensions and applicationsText L·452 min
Ch. XIIStatistical sampling4 texts · 0 read
  • Populations, censuses and samplesText L·463 min
  • Random sampling methodsText L·473 min
  • Non-random sampling methodsText L·482 min
  • Sampling and the large data setText L·492 min
Ch. XIIIData presentation and interpretation4 texts · 0 read
  • Measures of location and spreadText L·502 min
  • Representing data: histograms and box plotsText L·513 min
  • Outliers and cleaning dataText L·523 min
  • Correlation and regressionText L·533 min
Ch. XIVProbability4 texts · 0 read
  • Events, sample spaces and the addition ruleText L·542 min
  • Venn diagrams and set notationText L·552 min
  • Conditional probabilityText L·562 min
  • Tree diagrams and independenceText L·572 min
Ch. XVStatistical distributions4 texts · 0 read
  • Discrete random variablesText L·582 min
  • The binomial distributionText L·592 min
  • The normal distributionText L·602 min
  • Modelling and choosing a distributionText L·613 min
Ch. XVIStatistical hypothesis testing4 texts · 0 read
  • The logic of hypothesis testingText L·623 min
  • Testing a binomial proportionText L·633 min
  • Correlation hypothesis testsText L·642 min
  • Testing a normal meanText L·653 min
Ch. XVIIQuantities and units in mechanics3 texts · 0 read
  • SI units and derived quantitiesText L·662 min
  • Modelling assumptions in mechanicsText L·673 min
  • Scalars, vectors and dimensional reasoningText L·683 min
Ch. XVIIIKinematics5 texts · 0 read
  • Motion graphsText L·693 min
  • The constant-acceleration equationsText L·702 min
  • Motion under gravityText L·712 min
  • Variable acceleration and calculusText L·722 min
  • ProjectilesText L·732 min
Ch. XIXForces and Newton's laws4 texts · 0 read
  • Forces, resultants and equilibriumText L·743 min
  • Newton's laws and F = maText L·753 min
  • Friction and the inclined planeText L·763 min
  • Connected particlesText L·773 min
Ch. XXMoments4 texts · 0 read
  • The moment of a forceText L·783 min
  • The principle of moments and equilibriumText L·792 min
  • Rods, beams and reactionsText L·803 min
  • Tilting and limiting equilibriumText L·813 min
Reading progress · subject
—Read
0/81
Texts
~195
min total
Recommended start
Overarching themes · Ch. I
Mathematical argument, language and proof (OT1)
Text L·01 · 3 min
Read now
Instrument · 01Recommended study order
  1. 1Overarching themes
  2. 2Proof
  3. 3Algebra and functions
  4. 4Coordinate geometry in the (x, y) plane
  5. 5Sequences and series
  6. 6Trigonometry
  7. 7Exponentials and logarithms
  8. 8Differentiation
  9. 9Integration
  10. 10Numerical methods
  11. 11Vectors
  12. 12Statistical sampling
  13. 13Data presentation and interpretation
  14. 14Probability
  15. 15Statistical distributions
  16. 16Statistical hypothesis testing
  17. 17Quantities and units in mechanics
  18. 18Kinematics
  19. 19Forces and Newton's laws
  20. 20Moments
Instrument · 02Exam structure
Paper 1 — Pure Mathematics (AQA 7357/1)
2 hours, 100 marks, one third of the A-Level. Assesses any content from the pure core: proof, algebra and functions, coordinate geometry, sequences and series, trigonometry, exponentials and logarithms, differentiation, integration, numerical methods and vectors. A mix of short and multi-step extended questions; a scientific or graphical calculator is permitted (as on every paper).
Paper 2 — Pure Mathematics and Mechanics (AQA 7357/2)
2 hours, 100 marks, one third of the A-Level. Assesses the pure core again together with the mechanics content: quantities and units in mechanics, kinematics, forces and Newton's laws, and moments. Mechanics questions are frequently modelling questions in which assumptions must be stated and criticised.
Paper 3 — Pure Mathematics and Statistics (AQA 7357/3)
2 hours, 100 marks, one third of the A-Level. Assesses the pure core together with the statistics content: statistical sampling, data presentation and interpretation (including the prescribed large data set), probability, statistical distributions and hypothesis testing. Some questions are set in the context of the large data set students have studied.
Assessment objectives and grading
Across the three papers the assessment objectives are weighted approximately AO1 (use and apply standard techniques) 50%, AO2 (reason, interpret and communicate mathematically) 25%, and AO3 (solve problems within mathematics and in context, including modelling) 25%. The full A-Level is linear, graded A*–E (with U below E); AS Mathematics (7356) is a separate qualification graded A–E and does not count towards the A-Level.
Instrument · 03Official sources
  • Mathematics: AS and A level content (GCE subject content)Department for Education
  • AQA AS and A-level Mathematics (7356 / 7357) specificationAQA

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